Optimal stopping inequalities for the integral of Brownian paths (Q1269069)

The author derives inequalities for Brownian path integrals of the form \(E(\int_0^\tau F(|B_\tau |) dt)\) in terms of the expected value of the stopping time \(\tau\), resp. in terms of the expected value of some power of the stopping time. These inequalities are similar to the Burkholder-Davis inequality which is also a major tool in the derivation. Another tool is provided by solving an appropriate optimal stopping problem.